Darren Aronofsky made a strong impression in 1998 with Pi, his low-budget debut as writer-director, in which a number theorist descends into insanity as he searches for a mathematical solution to the secret of the universe. He followed this up with Requiem for a Dream, about four people in a rundown corner of New York whose dreams are destroyed by their addiction to drugs. His third film, the confused fantasy The Fountain, dealt with a 16th-century conquistador, a present-day American scientist and an astronaut in the 26th century searching for eternal life. This was followed by The Wrestler, a somewhat earthier study of an ageing practitioner of a despised, lowlife profession, much given to self-mutilation and prepared to risk his life in order to make the comeback that will restore some self‑respect.

His latest film, the glossy, hard-surfaced Black Swan, which he co-scripted with Mark Heyman, co-producer of The Wrestler, takes Aronofsky into the upper reaches of New York's social and artistic world but pursues themes and obsessions that inform his previous work. The central character is Nina Sayers (the beautifully glacial Natalie Portman), a young dancer who lives, eats and sleeps ballet. She starts the film having dreamt of appearing in Tchaikovsky's Swan Lake. She spends her days rehearsing with a corps de ballet at the Lincoln Centre. Shortly thereafter she's presented with a grand cake by her mother to celebrate having been tapped by Thomas (Vincent Cassel), the Svengali-like head of the company, to play Odette/Odile in his new Swan Lake, but, in a neurotic gesture, she only eats a small creamy piece of it from her mother's finger.

The film has certain superficial resemblances to Herbert Ross's ballet movie, The Turning Point, in that the heroine's mother (Barbara Hershey) is an ex-dancer who gave up a career to raise a daughter in whom all her hopes are invested. But this aspect is dealt with only superficially. In some ways it is closer in tone to that peak of all dance films, Powell and Pressburger's The Red Shoes, in embracing the romantic notion of ballet as a demanding, all-consuming vocation that can lead to destruction and death. But Aronofsky seems little interested in either the internal dynamics of a dance company or in the creation of a specific work for the stage. We are told that this production of Swan Lake is a bid to restore the fortunes of a failing company, but we do not discover, and can only vaguely infer, what Thomas's particular innovations are beyond some sort of psychological realism. Because Natalie Portman is not a professional dancer she cannot be exposed to the lengthy scrutiny that Moira Shearer and company are in The Red Shoes or Leslie Browne and the electrifying Mikhail Baryshnikov in The Turning Point, so we only get brief segments of the ballet. We have to accept Nina's excellence or otherwise when Thomas comments on it sarcastically in rehearsal and when the audience gives her standing ovations during the crisis-driven premiere performance.

What we have in Black Swan is a psychodrama of a rather obvious kind, and an equally traditional theatrical tale in which the off-stage life of an artist mirrors the on-stage performance until the point is reached where the two merge. From the start Nina is a troubled person, given to seeing her doppelganger during her journeys to and from work. When she is told to get in touch with her dark side so she can convince as Odile, the evil black swan, as well as Odette, the good white one, this dual identity becomes an obsession. In a rather overly neat way, which is directly identified in the film's final credits, everyone around Nina assumes, in her fraught mind, a role in Swan Lake, her mother becoming the Queen, choreographer Thomas the Gentleman, and Lily (Mila Kunis), the rival dancer for her role, the Black Swan. Just as the roles become confused, so Nina herself moves towards what resembles a clinical breakdown in which she can't distinguish fantasy from reality. For a moment at least, the audience shares her confusion. As her paranoia develops, the film enters familiar horror movie territory.

Like the fighter played by Mickey Rourke in The Wrestler, Nina turns to self-mutilation, as if it were not enough that her toes should bleed. In her quest for some form of absolute perfection of the sort the mathematician in Aronofsky's Pi seeks, her body becomes a treacherous enemy to be combated. Natalie Portman gives a performance of painful intensity that conveys not just someone in the pursuit of artistic excellence but a person driven over the edge, with the audience invited to accompany her on the journey. But there is a dangerous fallacy here, and it is embodied in the character of Thomas. He is the agent by which her delicate balance is disturbed through his insistence that she must discover her dark side by some form of physical and spiritual abandonment. By implication the solution resides in polymorphous perverse sex. This is playing with the idea that you must go mad to play Lear or commit murder to convince as Othello or Macbeth.

Black Swan holds the attention in a manipulative manner, but one can see in it the possibility of a better, more satisfying film with the same setting and the same dramatis personae. This would, for instance, have freed Winona Ryder from a melodramatic contrivance which is thrust upon her and allowed her to give a truly serious performance as a forty-something prima ballerina on the point of forced retirement. Instead, what Aronofsky has ended up with is an exercise in the higher kitsch, a slick, pretentious film in which the polished surface is a distorting mirror.

The director of The Wrestler and Requiem for a Dream tells Jason Solomons about capturing the intensity of ballet for his new horror film, Black Swan, and why his film-making is inspired by Bruce Springsteen's one-legged dog